Here, we analyze the ratio between the energy densities of DM and DE, defined as \(\mathrm {R}\equiv \mathrm {{\bar{\rho }}_{DM}}/\mathrm {{\bar{\rho }}_{DE}}\) .
From Eqs. () and (), we obtain [1]}, [2]}
\(\frac{\mathrm {d}R}{\mathrm {d}z}=\frac{-R}{(1+z)}\left(3\omega _{DE}+\frac{(1+R)\bar{Q}}{\bar{H}\rho _{DM}}\right).\) 
